Q 188 - Intermediate Algebra

Question

In the following exercises, factor completely using the difference of squares pattern, if possible.
$m^4-n^4$

Step-by-Step Solution

Answer

The complete factor of ploynomial is  $\left(m-n\right)\left(m+n\right)\left(m^2+n^2\right)$.

Step 1. Given information

Consider the given ploynomial 

$m^4-n^4$

Step 2. Formula used

$a^2-b^2=\left(a+b\right)\left(a-b\right)$

Step 3. Write the polynomial as squares.

Write the polynomial as perfect squared form. 

$m^4-n^4=\left({\left(m^2\right)}^2-{\left(n^2\right)}^2\right)$

Write them as product of conjugate.  

$$\begin{gathered} {\left(m^2\right)}^2-{\left(n^2\right)}^2=\left(m^2-n^2\right)\left(m^2+n^2\right) \\ =\left(m-n\right)\left(m+n\right)\left(m^2+n^2\right) \end{gathered}$$